# Clopper-Pearson Confidence Interval for Failures Which are Tackled by Countermeasures

### Description

Provides the extended Clopper-Pearson confidence limits for a failure model, where countermeasures are introduced.

### Usage

1 2 | ```
cm.clopper.pearson.ci(n, size, cm.effect, alpha = 0.1, CI = "upper", uniroot.lower = 0,
uniroot.upper = 1, uniroot.maxiter = 1e+05, uniroot.tol = 1e-10)
``` |

### Arguments

`n` |
sample size. |

`size` |
vector of the number of failures for each type. |

`cm.effect` |
vector of the success probabilities to solve a failure for each type. Corresponds to the probabilities |

`alpha` |
significance level for the |

`CI` |
indicates the kind of the confidence interval, options: "upper" (default), "lower", "two.sided". |

`uniroot.lower` |
The value of the |

`uniroot.upper` |
The value of the |

`uniroot.maxiter` |
The value of the |

`uniroot.tol` |
The value of the |

### Details

This is an extension of the Clopper-Pearson confidence interval, where different outcome scenarios of the random sampling are weighted by generalized binomial probabilities. The weights are the probabilities for observing *0,...,k* failures after the introduction of countermeasures.
Computes the confidence limits for the *p* of a binomial distribution, where *p* is the failure probability. The failures are tackled by countermeasures for specific failure types with different effectivity.
See the references for further information.

### Value

A data frame containing the kind of the confidence interval, upper and lower limits and the used significance level `alpha`

.

### References

D.Kurz, H.Lewitschnig, J.Pilz, *Decision-Theoretical Model for Failures which are Tackled by Countermeasures*, IEEE Transactions on Reliability, Vol. 63, No. 2, June 2014.

### See Also

`uniroot`

, `dgbinom`

, `clopper.pearson.ci`

### Examples

1 2 3 4 5 6 7 | ```
## n=110000 tested devices, 2 failures divided in 2 failure types k1=1, k2=1.
## 2 countermeasures with effectivities p1=0.5, p2=0.8
cm.clopper.pearson.ci(110000,size=c(1,1),cm.effect=c(0.5,0.8))
# Confidence.Interval = upper
# Lower.limit = 0
# Upper.limit = 3.32087e-05
# alpha = 0.1
``` |